CONCLUSIONES

Manufacturing variations can also lead to loss in quality due to performance degradation, non-conformance to specifications, high cost of redesign or scrap and failure. Due to such variations, the manufactured product may differ from the proposed ideal design and its per- formance may be sensitive to manufacturing uncertainty. To assure that a product meets the design specification, manufacturers select tight tolerances or a higher precision manufac- turing process, which can lead to considerable increase in manufacturing cost. Hence, it is important to consider the effect of manufacturing variations on a product during the design phase and select a design that isrobust.

3.4.1 Process Capability Data

More often than not design engineers do not have enough information about the downstream manufacturing process capability (Tata & Thornton, 1999). In recent years there have been many attempts to provide the designer with process capability data (Kotz & Johnson, 2002). Process Capability is the expected probability distribution of the manufactured products using a manufacturing process in ideal conditions (Bothe, 2001). Numerous methods for measuring process capability exist in the manufacturing literature; for example see Chase & Parkinson (1991); Boyles (1991); Kotz & Lovelace (1998); Bothe (2001). The most common quantitative definition of process capability is the process spread, or 6σp. The performance of a manufacturing process can be measured using the dimensions of parts produced by the process. In the limiting case, the process is assumed to have a normal distribution with standard deviation σ. In practice, the observed variations in the process will be greater than that predicted by process capability due to temperature variations, tool wear, material properties etc, see figure 3.12. Moreover they are never strictly Gaussian in nature.

Probabilistic analysis have shown substantial degradation in performance of compressor blades in presence of manufacturing variations, errors and tolerances (Garzon, 2003; Lamb, 2005). These studies re-emphasize the need to consider robustness of compressor blade performance against manufacturing uncertainty in the design stage. The most common processes used for manufacturing compressor blades are flank milling and point milling and their process capability data can be readily made available to the designers. Next we discuss how to use such data for simulating manufacturing process variability and to understand its effect on aerodynamic performance of compressor blades.

Chapter 3 Effect of Geometry Variations on Compressor Blades 37

Observed Process Capability Ideal Process Capability

Tolerance = ∆h

µ

µ − 6σ µ + 6σ

Figure 3.12: Ideal and Observed Process Capability

3.4.2 Geometry Modeling of Manufacturing Variations

Once a manufacturing process is fixed (flank or point milling) and the process capability is known, manufacturing variations can be modeled. Figure 3.13 shows a typical manufacturing uncertainty band around the nominal compressor blade. The task at hand is to simulate a manufacturing process such that the observed manufactured blades have a normal distribu- tion with 6σp = ∆h. To model manufacturing uncertainty precisely, a parametric geometry model is sought which can describe geometry variations in the given tolerance band around the nominal geometry. These could be variations in chord, camber and thickness. Here we present an efficient method using a combination of Hick-Hennes functions and splines for modeling manufacturing variations. To parametrize the blade section geometry we use a linear combination of Hicks-Henne functions super-imposed on a baseline shape. For the problem under consideration, we have used 10 Hicks-Henne functions to parametrize the compressor fan blade. The Hicks-Henne shape functions can also be expressed as

bi(x) =sin2(πxmi_{) , m}

i=ln(0.5)/ln(xMi) i= 1,2, ...n (3.4)

wherexis the normalized chord-wise coordinate starting from the trailing edge encompassing the whole airfoil and back to the trailing edge. (0 ≤ x ≤ 1), xMi are preselected values

Chapter 3 Effect of Geometry Variations on Compressor Blades 38

Nominal Geometry

Tolerance Band

Δh

Figure 3.13: Manufacturing uncertainty band in compressor blade

corresponding to the location of the maxima andn is the number of Hicks-Henne functions used.

In the present study, the locations of xMi for i = 1,2, ...,10 are chosen in a manner to

ensure clustering near the leading edge. This ensures more points where the curvature is higher and thus more variety in shapes near the leading edge. Each Hicks-Henne function is multiplied by a weight factor Wi |i= 1,2, ...,10, which controls the amplitude (maxima) of the respective functions. These weight factors give us 10 design variables to parametrize manufacturing uncertainty in the blade geometry. Note that though each Wi would have a effect on the whole shape of the blade, its maximum influence would be near the region corresponding to the location of its respective maxima (xMi). Figure 3.14 shows the location

of the maximum influence point due to each variable on the blade shape. Furthermore, two control points required are chosen to be the two points at the cusp on the trailing edge. This ensures that we also achieve deviations in the chord length of the airfoil. Some typical patterns of blade geometries obtained using the above method is shown in figure 3.15.

Figure 3.16 shows zoomed in view near the leading and trailing edge for two typical shapes obtained by using the above mentioned technique. Note that we obtain changes in chord length, which is not possible in the existing Hick-Henne based techniques. This is

Chapter 3 Effect of Geometry Variations on Compressor Blades 39 W5 W2 W1 W3 W4 W6 W7 W10 W9 W8 Chord

Figure 3.14: Maximum impact location due to each variable on the blade shape

achieved by having both the control points at the cusp of the trailing edge. The details of the implementation of this technique is fiven in Appendix B.

3.4.3 Probabilistic Analysis in Presence of Manufacturing Uncertainty

Once the manufacturing geometry simulation model is developed we combine it with PADRAM and the HYDRA suite of codes. The process defined in the flowchart given in figure 3.10 is executed. An LPτ based DOE of 150 points (shapes) is executed to understand the effect of manufacturing variations on the aerodynamic performance of the compressor blade. The choice of 150 points is again based on the fact that we are limited by the high computational cost involved in running the CFD solver and that we need at least 10 points for each design variable.

The CFD analysis for all these blade shapes is conducted using HYDRA. Figure 3.17 shows the normalized scatter in the aerodynamic performance due to manufacturing uncertainty.

Chapter 3 Effect of Geometry Variations on Compressor Blades 40

Figure 3.15: Some typical manufacturing variations shape s obtained using the parametric

model

It can be observed that for the selected value of process capability (σp) we observe upto 6% deterioration in the pressure loss coefficient. Later in the thesis we will discuss methods to alleviate this issue. It is also interesting to observe that some blades show improvement in performance.